Skulltulas are less dangerous when they are on the ground. They are very easy to dispatch of as it only really takes two hits to kill them, an upward slash to knock them onto their backs and a final Fatal Blow to kill them. If you ever get the chance to do so, cut them off their webs to kill them, it's very easy to accidentally get hit when you attack them and rebound.
They (AFAIK) only come in two forms, hanging on a web string and will go down to your level when you get close or on a full web usually facing you.
When on a string, you could use your Beetle on the string to cut them down. Otherwise if you don't have it (or don't want to pull it out and rather fight them), you need to find a way to turn them so you can attack their weak spot, their bellies. To do that, do one horizontal slash (in either direction) so they are knocked to the side and spin around. After they spin (you may need to wait a bit), they should be turned around so their bellies are facing you. When that happens, do straight stabs forward to attack and kill them. Just be careful of the rebounds when they swing.
When on the webs, you have a couple of options. It should be easier to get past them as they usually don't move.
If they're on a web but are sitting at ground level, try to get behind them if possible so you could forward stab them in their bellies. If not, you'll have to cut them down so you can fight them on the ground. Just cut at their webs and they'll eventually get off to fight.
If they're on a web but not at ground level, you can actually just go though the web with relative ease. Run toward the web and at the last second, roll (shake the nunchuk). You should be able to perform the roll almost completely through. You'll get caught in the web for a second but will break free almost immediately. At this point you could go on or turn around and finish it off using the strategies when they're at ground level.
You won't be able to access them yet. The earliest you can would be your second visit to the forest...
after you have obtained the Water Dragon's Scale allowing you to swim. You'll have to climb the tree from the inside so you could drop down and reach those cubes.
The target you are referring to is a target for the Clawshots. These come even later in the game and allows you to zoom up to the target.
These are obtained by passing the second goddess trial.
Best Answer
You're supposed to make it dizzy by rotating your sword in a circle (not a spin attack). Do it quickly, but not too quickly—if you go too fast, you'll start doing random swings, which won't work.
For the eyes that appear later in the temple, you need to have all of the eyes in a given room look at you at the same time in order to get past them. If not all of the eyes are open, they won't get dizzy and die no matter how fast you rotate your sword.